<p>This dissertation studies the optimal control of two different dynamic systems with learning: (i) diagnostic service systems, and (ii) green incentive policy design. In both cases, analytical models have been developed to improve our understanding of the system, and managerial insights are gained on its optimal management.</p><p>We first consider a diagnostic service system in a queueing framework, where the service is in the form of sequential hypothesis testing. The agent should dynamically weigh the benefit of performing an additional test on the current task to improve the accuracy of her judgment against the incurred delay cost for the accumulated workload. We analyze the accuracy/congestion tradeoff in this setting and fully characterize the structure of the optimal policy. Further, we allow for admission control (dismissing tasks from the queue without processing) in the system, and derive its implications on the structure of the optimal policy and system's performance.</p><p>We then study Feed-in-Tariff (FIT) policies, which are incentive mechanisms by governments to promote renewable energy technologies. We focus on two key network externalities that govern the evolution of a new technology in the market over time: (i) technological learning, and (ii) social learning. By developing an intertemporal model that captures these dynamics, we investigate how lawmakers should leverage on such effects to make FIT policies more efficient. We contrast our findings against the current practice of FIT-implementing jurisdictions, and also determine how the FIT regimes should depend on specific technology and market characteristics.</p> / Dissertation

Cognitive Radios are emerging communication systems which efficiently utilize the unused licensed radio spectrum called spectral holes. They run Spectrum sensing algorithms to identify these spectral holes. These holes need to be identified at very low SNR (<=-20 dB) under multipath fading, unknown channel gains and noise power. Cooperative spectrum sensing which exploits spatial diversity has been found to be particularly effective in this rather daunting endeavor. However despite many recent studies, several open issues need to be addressed for such algorithms. In this thesis we provide some novel cooperative distributed algorithms and study their performance. We develop an energy efficient detector with low detection delay using decentralized sequential hypothesis testing. Our algorithm at the Cognitive Radios employ an asynchronous transmission scheme which takes into account the noise at the fusion center. We have developed a distributed algorithm, DualSPRT, in which Cognitive Radios (secondary users) sequentially collect the observations, make local decisions and send them to the fusion center. The fusion center sequentially processes these received local decisions corrupted by Gaussian noise to arrive at a final decision. Asymptotically, this algorithm is shown to achieve the performance of the optimal centralized test, which does not consider fusion center noise. We also theoretically analyze its probability of error and average detection delay. Even though DualSPRT performs asymptotically well, a modification at the fusion node provides more control over the design of the algorithm parameters which then performs better at the usual operating probabilities of error in Cognitive Radio systems. We also analyze the modified algorithm theoretically. DualSPRT requires full knowledge of channel gains. Thus we extend the algorithm to take care the imperfections in channel gain estimates. We also consider the case when the knowledge about the noise power and channel gain statistic is not available at the Cognitive Radios. This problem is framed as a universal sequential hypothesis testing problem. We use easily implementable universal lossless source codes to propose simple algorithms for such a setup. Asymptotic performance of the algorithm is presented. A cooperative algorithm is also designed for such a scenario. Finally, decentralized multihypothesis sequential tests, which are relevant when the interest is to detect not only the presence of primary users but also their identity among multiple primary users, are also considered. Using the insight gained from binary hypothesis case, two new algorithms are proposed.

Le problème étudié dans le cadre de cette thèse porte essentiellement sur l'étape de détection de défaut dans un processus de diagnostic industriel. Ces travaux sont motivés par la surveillance de deux sous-systèmes complexes d'un autobus impactant la disponibilité des véhicules et leurs coûts de maintenance : le système de freinage et celui des portes. Cette thèse décrit plusieurs outils dédiés au suivi de fonctionnement de ces deux systèmes. On choisit une approche de diagnostic par reconnaissance des formes qui s'appuie sur l'analyse de données collectées en exploitation à partir d'une nouvelle architecture télématique embarquée dans les autobus. Les méthodes proposées dans ces travaux de thèse permettent de détecter un changement structurel dans un flux de données traité séquentiellement, et intègrent des connaissances disponibles sur les systèmes surveillés. Le détecteur appliqué aux freins s'appuie sur les variables de sortie (liées au freinage) d'un modèle physique dynamique du véhicule qui est validé expérimentalement dans le cadre de nos travaux. L'étape de détection est ensuite réalisée par des cartes de contrôle multivariées à partir de données multidimensionnelles. La stratégie de détection pour l'étude du système porte traite directement les données collectées par des capteurs embarqués pendant des cycles d'ouverture et de fermeture, sans modèle physique a priori. On propose un test séquentiel à base d'hypothèses alimenté par un modèle génératif pour représenter les données fonctionnelles. Ce modèle de régression permet de segmenter des courbes multidimensionnelles en plusieurs régimes. Les paramètres de ce modèle sont estimés par un algorithme de type EM dans un mode semi-supervisé. Les résultats obtenus à partir de données réelles et simulées ont permis de mettre en évidence l'efficacité des méthodes proposées aussi bien pour l'étude des freins que celle des portes / This thesis is mainly dedicated to the fault detection step occurring in a process of industrial diagnosis. This work is motivated by the monitoring of two complex subsystems of a transit bus, which impact the availability of vehicles and their maintenance costs: the brake and the door systems. This thesis describes several tools that monitor operating actions of these systems. We choose a pattern recognition approach based on the analysis of data collected from a new IT architecture on-board the buses. The proposed methods allow to detect sequentially a structural change in a datastream, and take advantage of prior knowledge of the monitored systems. The detector applied to the brakes is based on the output variables (related to the brake system) from a physical dynamic modeling of the vehicle which is experimentally validated in this work. The detection step is then performed by multivariate control charts from multidimensional data. The detection strategy dedicated to doors deals with data collected by embedded sensors during opening and closing cycles, with no need for a physical model. We propose a sequential testing approach using a generative model to describe the functional data. This regression model allows to segment multidimensional curves in several regimes. The model parameters are estimated via a specific EM algorithm in a semi-supervised mode. The results obtained from simulated and real data allow to highlight the effectiveness of the proposed methods on both the study of brakes and doors

Our vision is as yet unsurpassed by machines because of the sophisticated representations of objects in our brains. This representation is vastly different from a pixel-based representation used in machine storages. It is this sophisticated representation that enables us to perceive two faces as very different, i.e, they are far apart in the “perceptual space”, even though they are close to each other in their pixel-based representations. Neuroscientists have proposed distances between responses of neurons to the images (as measured in macaque monkeys) as a quantification of the “perceptual distance” between the images. Let us call these neuronal dissimilarity indices of perceptual distances. They have also proposed behavioural experiments to quantify these perceptual distances. Human subjects are asked to identify, as quickly as possible, an oddball image embedded among multiple distractor images. The reciprocal of the search times for identifying the oddball is taken as a measure of perceptual distance between the oddball and the distractor. Let us call such estimates as behavioural dissimilarity indices. In this thesis, we describe a decision-theoretic model for visual search that suggests a connection between these two notions of perceptual distances. In the first part of the thesis, we model visual search as an active sequential hypothesis testing problem. Our analysis suggests an appropriate neuronal dissimilarity index which correlates strongly with the reciprocal of search times. We also consider a number of alternative possibilities such as relative entropy (Kullback-Leibler divergence), the Chernoff entropy and the L1-distance associated with the neuronal firing rate profiles. We then come up with a means to rank the various neuronal dissimilarity indices based on how well they explain the behavioural observations. Our proposed dissimilarity index does better than the other three, followed by relative entropy, then Chernoff entropy and then L1 distance. In the second part of the thesis, we consider a scenario where the subject has to find an oddball image, but without any prior knowledge of the oddball and distractor images. Equivalently, in the neuronal space, the task for the decision maker is to find the image that elicits firing rates different from the others. Here, the decision maker has to “learn” the underlying statistics and then make a decision on the oddball. We model this scenario as one of detecting an odd Poisson point process having a rate different from the common rate of the others. The revised model suggests a new neuronal dissimilarity index. The new dissimilarity index is also strongly correlated with the behavioural data. However, the new dissimilarity index performs worse than the dissimilarity index proposed in the first part on existing behavioural data. The degradation in performance may be attributed to the experimental setup used for the current behavioural tasks, where search tasks associated with a given image pair were sequenced one after another, thereby possibly cueing the subject about the upcoming image pair, and thus violating the assumption of this part on the lack of prior knowledge of the image pairs to the decision maker. In conclusion, the thesis provides a framework for connecting the perceptual distances in the neuronal and the behavioural spaces. Our framework can possibly be used to analyze the connection between the neuronal space and the behavioural space for various other behavioural tasks.